* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices

http://cyber.sibsutis.ru:82/Monarev/docs/nauka/PROBABILITY/Kallenberg%20O.%20Foundations%20of%20Modern%20Probability%20(Springer,1997)(ISBN%200387949577)(535s).pdf

Foundations of modern probability

We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

/pdf/approximate-nearest-neighbors-towards-removing-the-curse-of-27lmlz5prr.pdf

Approximate nearest neighbors: towards removing the curse of dimensionality

Rod Borup is a Team Leader in the fuel cell program at Los Alamos National Lab in Los Alamos, New Mexico. He received his B.S.E. in Chemical Engineering from the University of Iowa in 1988 and his Ph.D. from the University of Washington in 1993. He has worked on fuel cell technology since 1994, working in the areas of hydrogen production and PEM fuel cell stack components. He has been awarded 12 U.S. patents, authored over 40 papers related to fuel cell technology, and presented over 50 oral papers at national meetings. His current main research area is related to water transport in PEM fuel cells and PEM fuel cell durability. Recently, he was awarded the 2005 DOE Hydrogen Program R&D Award for the most significant R&D contribution of the year for his team's work in fuel cell durability and was the Principal Investigator for the 2004 Fuel Cell Seminar (San Antonio, TX, USA) Best Poster Award. Jeremy Meyers is an Assistant Professor of materials science and engineering and mechanical engineering at the University of Texas at Austin, where his research focuses on the development of electrochemical energy systems and materials. Prior to joining the faculty at Texas, Jeremy workedmore » as manager of the advanced transportation technology group at UTC Power, where he was responsible for developing new system designs and components for automotive PEM fuel cell power plants. While at UTC Power, Jeremy led several customer development projects and a DOE-sponsored investigation into novel catalysts and membranes for PEM fuel cells. Jeremy has coauthored several papers on key mechanisms of fuel cell degradation and is a co-inventor of several patents. In 2006, Jeremy and several colleagues received the George Mead Medal, UTC's highest award for engineering achievement, and he served as the co-chair of the Gordon Research Conference on fuel cells. Jeremy received his Ph.D. in Chemical Engineering from the University of California at Berkeley and holds a Bachelor's Degree in Chemical Engineering from Stanford University. Bryan Pivovar received his B.S. in Chemical Engineering from the University of Wisconsin in 1994. He completed his Ph.D. in Chemical Engineering at the University of Minnesota in 2000 under the direction of Profs. Ed Cussler and Bill Smyrl, studying transport properties in fuel cell electrolytes. He continued working in the area of polymer electrolyte fuel cells at Los Alamos National Laboratory as a post-doc (2000-2001), as a technical staff member (2001-2005), and in his current position as a team leader (2005-present). In this time, Bryan's research has expanded to include further aspects of fuel cell operation, including electrodes, subfreezing effects, alternative polymers, hydroxide conductors, fuel cell interfaces, impurities, water transport, and high-temperature membranes. Bryan has served at various levels in national and international conferences and workshops, including organizing a DOE sponsored workshop on freezing effects in fuel cells and an ARO sponsored workshop on alkaline membrane fuel cells, and he was co-chair of the 2007 Gordon Research Conference on Fuel Cells. Minoru Inaba is a Professor at the Department of Molecular Science and Technology, Faculty of Engineering, Doshisha University, Japan. He received his B.Sc. from the Faculty of Engineering, Kyoto University, in 1984 and his M.Sc. in 1986 and his Dr. Eng. in 1995 from the Graduate School of Engineering, Kyoto University. He has worked on electrochemical energy conversion systems including fuel cells and lithium-ion batteries at Kyoto University (1992-2002) and at Doshisha University (2002-present). His primary research interest is the durability of polymer electrolyte fuel cells (PEFCs), in particular, membrane degradation, and he has been involved in NEDO R&D research projects on PEFC durability since 2001. He has authored over 140 technical papers and 30 review articles. Kenichiro Ota is a Professor of the Chemical Energy Laboratory at the Graduate School of Engineering, Yokohama National University, Japan. He received his B.S.E. in Applied Chemistry from the University of Tokyo in 1968 and his Ph.D. from the University of Tokyo in 1973. He has worked on hydrogen energy and fuel cells since 1974, working on materials science for fuel cells and water electrolysis. He has published more than 150 original papers, 70 review papers, and 50 scientific books. He is now the president of the Hydrogen Energy Systems Society of Japan, the chairman of the Fuel Cell Research Group of the Electrochemical Society of Japan, and the chairman of the National Committee for the Standardization of the Stationary Fuel Cells. ABSTRACT TRUNCATED« less

Scientific aspects of polymer electrolyte fuel cell durability and degradation.

We consider linear equations y = Φx where y is a given vector in ℝn and Φ is a given n × m matrix with n 0 so that for large n and for all Φ's except a negligible fraction, the following property holds: For every y having a representation y = Φx0by a coefficient vector x0 ∈ ℝmwith fewer than ρ · n nonzeros, the solution x1of the 1-minimization problem



is unique and equal to x0. In contrast, heuristic attempts to sparsely solve such systems—greedy algorithms and thresholding—perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almost-spherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices. © 2006 Wiley Periodicals, Inc.

For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution

We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candes and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finite-dimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result, we obtain simple and direct proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements have a certain universality with respect to the sparsity-inducing basis.

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A Simple Proof of the Restricted Isometry Property for Random Matrices

Extensions of Lipschitz mappings into a Hilbert space

Basic concepts in the geometry of Banach spaces (W.B. Johnson, J. Lindenstrauss). Positive operators (Y.A. Abramovitch, C.D. Aliprantis). Lp spaces (D. Alspach, E. Odell). Convex geometry and functional analysis (K. Ball). A p-sets in analysis: Results, problems and related aspects (J. Bourgain). Martingales and singular integrals in Banach spaces (D.L. Burkholder). Approximation properties (P.G. Casazza). Local operator theory, random matrices and Banach spaces (K.R. Davidson, S.J. Szarek). Applications to mathematical finance (F. Delbaen). Perturbed minimization principles and applications (R. Deville, N. Ghoussoub). Operator ideals (J. Diestel, H. Jarchow, A. Pietsch). Special Banach lattices and their applications(S.J. Dilworth). Some aspects of the invariant subspace problem (P. Enflo,V. Lomonosov). Special bases in function spaces (T. Figel, P. Wojtaszczyk). Infinite dimensional convexity (V. Fonf, J. Lindenstrauss, R.R. Phelps). Uniform algebras as Banach spaces (T.W. Gamelin, S.V. Kisliakov). Euclidean structure in finite dimensional normed spaces (A.A. Giannopoulos, V.D. Milman). Renormings of Banach spaces (G. Godefroy). Finite dimensional subspaces of Lp (W.B. Johnson, G. Schechtman). Banach spaces and classical harmonic analysis (S.V. Kisliakov). Aspects of the isometric theory of Banach spaces (A. Koldobsky, H. Konig). Eigenvalues of operators and applications (H. Konig).

Handbook of the Geometry of Banach spaces

Factoring weakly compact operators

Since the end of World War II, we have witnessed the development of solid-state batteries as rechargeable energy storage devices with high power density; a revolution in high-temperature electrochemical sensors in environmental, industrial, and energy efficiency control; and the introduction of fuel cells to avoid the Carnot inefficiency inherent in noncatalytic energy conversion. The trend away from corrosive aqueous solutions and toward solid-state technologywas inevitable in electrochemical energy engineering, if only for convenience and safety in bulk handling. As a consequence, the characterization of systems with solid–solid or solid–liquid interfaces, often involving solid ionic conductors and frequently operating well above room temperature, has become a major concern of electrochemists and materials scientists. At an interface, physical properties—crystallographic, mechanical, compositional, and, particularly, electrical—change precipitously, and heterogeneous charge distributions (polarizations) reduce the overall electrical conductivity of a system. Proliferation of interfaces is a distinguishing feature of solid-state electrolytic cells, where not only is the junction between electrode and electrolyte considerably more complex than in aqueous cells but also the solid electrolyte is commonly polycrystalline. Each interface will polarize in its unique way when the system is subjected to an applied potential difference. The rate at which a polarized region will change when the applied voltage is reversed is characteristic of the type of interface: slow for chemical reactions at the triple-phase contacts between atmosphere, electrode, and electrolyte, appreciably faster across grain boundaries in the polycrystalline electrolyte. The emphasis in electrochemistry has consequently shifted from a time/concentration dependency to frequency-related phenomena, a trend toward small-signal alternating current (ac) studies. Electrical double layers and their inherent capacitive reactances are characterized by their relaxation times ormore realistically by the distribution of their relaxation times. The electrical response of a heterogeneous cell can vary substantially depending on the species of charge present, the microstructure of the electrolyte, and the texture and nature of the electrodes. Impedance spectroscopy (IS) is a relatively new and powerful method of characterizing many of the electrical properties of materials and their interfaces with electronically conducting electrodes. It may be used to investigate the dynamics of bound or mobile charge in the bulk or interfacial regions of

Fundamentals of Impedance Spectroscopy

https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1033&context=enme_facpub

William B. Johnson

Papers

Extensions of Lipschitz mappings into a Hilbert space

Handbook of the Geometry of Banach spaces

Factoring weakly compact operators

Fundamentals of Impedance Spectroscopy

Mechanical response of fuel cell membranes subjected to a hygro-thermal cycle